Copy pasting sentences from abstracts of other papers for describing related work

So I am thinking about copy-pasting two or three sentences from the abstract of each referenced paper.

This seems absolutely appropriate, as long as you quote them correctly. Which brings us to:

I have read that it may be a good idea to put quotes, but I find quotes, especially their immoderate use, as bad style.

It is not only a good idea to do that, it is required. You need to make explicit that those are verbatim copies. The semantics of copying text from a paper and summarizing the key points yourself are different for a reader, and you need to make this difference explicit by demarking which parts you have taken in verbatim.

Can I get in trouble for this?

Yes.

I would not go that far in considering anything of this as plagiarism, as the work is referenced and I am not taking credit for someone else's work. Personally if one would do the same with my work, I would not be concerned at all, on the contrary, as long as not more than a few sentences are taken and the work is properly referenced, but you may have a different view.

This reminds me a bit of a few high-profile cases of plagiarisms that were going around lately in the german-speaking areas. Often, the excuses presented by the accused authors were similar ("hey, the text I copied wasn't really that important - it was just the introduction after all!", "I cited it anyway, I just did not make clear that the text is actually copied from there", etc.). These excuses never fly. Be rigorous with your handling of sources. Everything else is just playing with fire.

I cannot see that there is any exception to using quotes and providing the full, correct citation. It is honest and correct, anything less just doesn't cut it.